Batch rename shape keys
You can use the python api to script functionality, which isn't exposed through UI functions.

Write/Paste scripts in the text editor and press Run Script on the editor's menu bar to execute it.

First we get a list of shape_keys.

import bpy

# get the selected object
selected_object = bpy.context.object

# get its shapekeys
shape_keys = selected_object.data.shape_keys.key_blocks


Next, we can loop through the list and do a replace operation. shape_key.name is a string which stores/gets/sets the shapekeys name.

# loop through shapekeys and replace the names
for key in shape_keys:
    key.name = key.name.replace("Key", "FaceKey")


We could also suffix them with an indice.

# loop through shapekeys and replace the names
for index, key in enumerate(shape_keys):
    if key.name != "Basis":
        key.name = "MyKey" + str(index)


For some reason, the UI doesn't update the names of the shapekeys untill you hover over them.